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1. Take the first number and add it with the units digit of the second number.19+8=27

2. Multiply the result by 1027*10=270

3. Multiply the units digit of the first number with that of the second number9*8=72

4. Add the result of step 2 and 3 together270+72 = 342

It would be much better to know the multiplication tables of numbers up to 19. Numbers up to 19 are used often and knowing their tables can speed up your calculations considerably Then 18*19 is straight forward. 18*9 = 162. Write 2 and carry 1618*1 = 18. Add 16 to get 34. You get 342.

Also, learning tables is not as hard as you might imagine. e.g. 18*2 we know is 36. 18*3 is 18 more than 36

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1. Take the first number and add it with the units digit of the second number.19+8=27

2. Multiply the result by 1027*10=270

3. Multiply the units digit of the first number with that of the second number9*8=72

4. Add the result of step 2 and 3 together270+72 = 342

This is a translation of the algebraic multiplication of two numbers of the form 1a * 1b = (10+a)(10+b) = 100+10a+10b+ab. The latest expression we can also written it as (10+a+b)10+ab=(1a+b)10+ab.

I don't think the algorithm can be a real time saver. And its usage is quite limited (numbers below 20).Many times, depending on the numbers, we can find specific shortcuts. For example, 19 * 18 I would do it as (20 - 1) * 18 = 360 - 18 = 342, as it is always easy to multiply by 10 and 2.
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